标题： KPZ模型上尾路径测度的布朗桥极限 显示英文标题

标题： Brownian bridge limit of path measures in the upper tail of KPZ models

摘要： 对于KPZ普遍性类中的模型，如平面最后通过渗透（LPP）的零温度模型和定向聚合物的正温度模型，其上尾行为是近期研究的热点，特别关注相关的路径测度（即测地线或聚合物）。 对于指数LPP，扩散波动已在Basu-Ganguly中得到确立。 在定向景观中，LPP的连续极限，以及KPZ固定点在一点处的极限高斯性，以及相关有限维分布的极限，已通过Liu和Wang-Liu中的精确公式得到确立。 这些工作中进一步推测，相应的测地线的极限应为布朗桥。 我们在零温度和正温度下都证明了这一点；对于后者，之前既不知道一点极限，也不了解波动尺度。 我们没有依赖公式（因为在正温度文献中这些公式仍缺失），我们的论证是几何和概率性的，以Ganguly-Hegde关于上尾下权重和自由能轮廓形状的结果作为起点。 另一个关键要素涉及新颖的凝聚估计，这些估计是通过最近发现的这些模型中的平移不变性Borodin-Gorin-Wheeler开发的。 最后，我们的证明还揭示了在上尾条件下的聚合物测度结构，确立了一个围绕随机主干的淬火局部化指数。 显示英文摘要

摘要： For models in the KPZ universality class, such as the zero temperature model of planar last passage-percolation (LPP) and the positive temperature model of directed polymers, its upper tail behavior has been a topic of recent interest, with particular focus on the associated path measures (i.e., geodesics or polymers). For Exponential LPP, diffusive fluctuation had been established in Basu-Ganguly. In the directed landscape, the continuum limit of LPP, the limiting Gaussianity at one point, as well as of related finite-dimensional distributions of the KPZ fixed point, were established, using exact formulas in Liu and Wang-Liu. It was further conjectured in these works that the limit of the corresponding geodesic should be a Brownian bridge. We prove it in both zero and positive temperatures; for the latter, neither the one-point limit nor the scale of fluctuations was previously known. Instead of relying on formulas (which are still missing in the positive temperature literature), our arguments are geometric and probabilistic, using the results on the shape of the weight and free energy profiles under the upper tail from Ganguly-Hegde as a starting point. Another key ingredient involves novel coalescence estimates, developed using the recently discovered shift-invariance Borodin-Gorin-Wheeler in these models. Finally, our proof also yields insight into the structure of the polymer measure under the upper tail conditioning, establishing a quenched localization exponent around a random backbone.